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Mathematics - Elementary Curriculum Mathematics Grade 5
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Strand: NUMBER AND OPERATIONS - FRACTIONS (5.NF)

Use equivalent fractions as a strategy to add and subtract fractions (Standards 5.NF.12). Apply and extend previous understandings of multiplication and division to multiply and divide fractions (Standards 5.NF.37).

Standard 5.NF.1

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

  • Addition of Fractions Using a Visual Model
    Adding two fractions with unlike denominators is the focus of this video lesson. Students will learn how to use a visual model to work with these fractions. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
  • Calculation Nation
    Calculation Nation uses the power of the Web to let students challenge opponents from anywhere in the world. At the same time, students are able to challenge themselves by investigating significant mathematical content and practicing fundamental skills. The element of competition adds an extra layer of excitement.
  • Commutative and Associative Equations
    This lesson focuses on how to rearrange and combine parts of algebraic expressions by using the commutative and associative properties of addition. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
  • Egyptian Fractions
    Because the Egyptians represented fractions differently than we do, this task can help students understand that there can be many ways of representing the same number. This helps prepare them for writing algebraic expressions in 6th grade.
  • Finding Common Denominators to Add
    This task asks students to find and use two different common denominators to add two given fractions. It also ask students to draw pictures to help them to see why finding a common denominator is an important part of solving the given addition problems.
  • Finding Common Denominators to Subtract
    Part of this task asks students to use two different denominators to subtract fractions. The purpose of this is to help students realize that any common denominator will work, not just the least common denominator. They are also asked to draw pictures to help them see why finding a common denominator is important.
  • Fractions on a Line Plot
    The purpose of this task is for students to add unit fractions with unlike denominators and solve addition and subtraction problems involving fractions that have more than one possible solution.
  • Fractions with Borrowing
    This Teaching Channel video shows how students use decomposition to subtract fractions and mixed numbers. (14 min.)
  • Grade 5 Math Module 3: Addition and Subtraction of Fractions (EngageNY)
    In Module 3, students' understanding of addition and subtraction of fractions extends from earlier work with fraction equivalence and decimals. This module marks a significant shift away from the elementary grades' centrality of base ten units to the study and use of the full set of fractional units from Grade 5 forward, especially as applied to algebra.
  • Grade 5 Unit 4: Adding, Subtracting, Multiplying, and Dividing Fractions (Georgia Standards)
    Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators.
  • Jog-a-Thon
    The purpose of this task is to present students with a situation where it is natural to add fraction with unlike denominators; it can be used for either assessment or instructional purposes.
  • Make Your Own Fractions Worksheet
    This Teachers Corner page allows the teacher to create worksheets to give students practice with addition, subtraction, multiplication and division of fractions.
  • Making S'Mores
    The purpose of this instructional task is to motivate a discussion about adding fractions and the meaning of the common denominator. The different parts of the task have students moving back and forth between the abstract representation of the fractions and the meaning of the fractions in the context.
  • Mixed Numbers with Unlike Denominators
    The purpose of this task is to help students realize there are different ways to add mixed numbers and is most appropriate for use in an instructional setting.
  • Number and Operations - Fractions (5.NF) - Fifth Grade Core Guide
    The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Fifth Grade Mathematics - Number and Operations - Fractions (5.NF)
  • Sharing Chocolate
    This task was designed to include specific features that support access for all students and align to best practice for English Language Learner (ELL) instruction.
  • Subtraction of Fractions Using a Visual Model
    Students will learn how to subtract fractions with unlike denominators by using a visual model. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
  • To Multiply Or Not to Multiply, Variation 2
    This task was written as part of a collaborative project between Illustrative Mathematics, the Smarter Balanced Digital Library, and the Teaching Channel.


UEN logo http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialists - Trish  French or Molly  Basham and see the Mathematics - Elementary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.